The Graph of y&sup2 = f(x)

This applet investigates what happens if you plot y&sup2 = f(x) alongside y = f(x). It uses a cubic graph as f(x), but you can investigate the general behaviour of the function y&sup2 = f(x) for any single-valued function using this applet. You should notice the behaviour as f(x) just touches the x-axis, as it crosses the x-axis, and as it crosses the line y = 1.